## Recursos de colección

1. #### Some Sufficient Conditions for Analytic Functions to Belong to ${\mathcal{Q}}_{K,0}(p,q)$ Space

Meng, Xiaoge
This paper gives some sufficient conditions for an analytic function to belong to the space consisting of all analytic functions $f$ on the unit disk such ${\lim }_{|a|{\rightarrow}1}{\int}_{\!\mathbb{D}} {|{f}^{\prime }(z)|}^{p}{(1-{|z|}^{2})}^{q}K(g(z,a))dA(z)=0.$

2. #### Noncoherence of a Causal Wiener Algebra Used in Control Theory

Sasane, Amol
Let ${\mathbb{C}}_{\geq 0}:=\{s\in \mathbb{C}\mid \text{Re}(s)\geq 0\}$ , and let ${\mathcal{W}}^{+}$ denote the ring of all functions $f:{\mathbb{C}}_{\geq 0} \rightarrow \mathbb{C}$ such that $f(s)={f}_{a}(s)+\displaystyle{{\sum }_{k=0}^{\infty }{f}_{k}{e}^{-s{t}_{k}}}\,(s\in {\mathbb{C}}_{\geq 0})$ , where ${f}_{a}\in {L}^{1}(0,\infty ),\,{({f}_{k})}_{k\geq 0}\in {\ell }^{1}$ , and $0={t}_{0}< {t}_{1}< {t}_{2}< \cdots$ equipped with pointwise operations. (Here $\widehat{{\cdot}}$ denotes the Laplace transform.) It is shown that the ring ${\mathcal{W}}^{+}$ is not coherent, answering a question of Alban Quadrat. In fact, we present two principal ideals in the domain ${\mathcal{W}}^{+}$ whose intersection is not finitely generated.

3. #### $h$ -Stability of Dynamic Equations on Time Scales with Nonregressivity

Choi, Sung Kyu; Goo, Yoon Hoe; Koo, Namjip
We study the $h$ -stability of dynamic equations on time scales, without the regressivity condition on the right-hand side of dynamic equations. This means that we can include noninvertible difference equations into our results.

4. #### Weighted Composition Operators on Some Weighted Spaces in the Unit Ball

Fu, Xiaohong; Zhu, Xiangling
Let ${\mathbb{B}}_{n}$ be the unit ball of ${\mathbb{C}}^{n}$ , $H({\mathbb{B}}_{n})$ the space of all holomorphic functions in ${\mathbb{B}}_{n}$ . Let $u\in H({\mathbb{B}}_{n})$ and $\alpha$ be a holomorphic self-map of ${\mathbb{B}}_{n}$ . For $f\in H({\mathbb{B}}_{n})$ , the weigthed composition operator $u{C}_{\alpha }$ is defined by $(u{C}_{\alpha }f)(z)=u(z)f(\alpha (z)),z\in {\mathbb{B}}_{n}.$ The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.

5. #### On a Two-Variable $p$ -Adic ${l}_{q}$ -Function

Kim, Min-Soo; Kim, Taekyun; Park, D. K.; Son, Jin-Woo
We prove that a two-variable $p$ -adic ${l}_{q}$ -function has the series expansion ${l}_{p,q}(s,t,\chi )=\vspace{1pt}{([2]}_{q}/{[2]}_{F}){\sum }_{a=1,(p,a)=1}^{F}{(-1)}^{a}(\chi (a){q}^{a}/{\langle a+pt\rangle }^{s}){\sum }_{m=0}^{\infty }(\begin{smallmatrix}-s\\ \vspace{0pt}m\end{smallmatrix}){(F/\langle a+pt\rangle )}^{m}{E}_{m,{q}^{F}}^{\ast}$ which interpolates the values ${l}_{p,q}(-n,t,\chi )={E}_{n,{\chi }_{n},q}^{\ast}(pt)-{p}^{n}{\chi }_{n}(p)({[2]}_{q}/{[2]}_{{q}^{p}}){E}_{n,{\chi }_{n},{q}^{p}}^{\ast}(t)$ , whenever $n$ is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this note is due to Washington.

6. #### Multivariate $p$ -Adic Fermionic $q$ -Integral on ${\mathbb{Z}}_{p}$ and Related Multiple Zeta-Type Functions

Kim, Min-Soo; Kim, Taekyun; Son, Jin-Woo
In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz's type $q$ -Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz's type $p$ -zeta functions which interpolate multiple twisted Carlitz's type $q$ -Euler (Bernoulli) polynomials?” The aim of this paper is to give a partial answer to this problem. Furthermore we derive some interesting identities related to twisted $q$ -extension of Euler polynomials and multiple twisted Carlitz's type $q$ -Euler polynomials.

7. #### Modulus of Convexity, the Coeffcient $R(1,X)$ , and Normal Structure in Banach Spaces

Jiao, Hongwei; Guo, Yunrui; Wang, Fenghui
Let ${\delta }_{\text{X}}(\epsilon )$ and $R(1,X)$ be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space $X$ has normal structure if $2{\delta }_{X}(1+\epsilon )>\text{max}\{(R(1,x)-1)\epsilon ,1-(1-\epsilon /R(1,X)-1)\}$ for some $\epsilon \in [0,1]$ which generalizes the known result by Gao and Prus.

8. #### On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers

Alves, Claudianor O.; Souto, Marco A. S.
We prove that the semilinear elliptic equation $-\Delta u=f(u)$ , in $\Omega$ , $u=0$ , on $\partial \Omega$ has a positive solution when the nonlinearity $f$ belongs to a class which satisfies $\mu {t}^{q}\leq f(t)\leq C{t}^{p}$ at infinity and behaves like ${t}^{q}$ near the origin, where $1< q < (N+2)/(N-2)$ if $N\geq 3$ and $1< q< +\infty$ if $N=1,2$ . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of $p$ .

9. #### Differential Subordinations Associated with Multiplier Transformations

Cătaş, Adriana; Oros, Georgia Irina; Oros, Gheorghe
The authors introduce new classes of analytic functions in the open unit disc which are defined by using multiplier transformations. The properties of these classes will be studied by using techniques involving the Briot-Bouquet differential subordinations. Also an integral transform is established.

10. #### Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation

Alekseenko, Alexander M.
We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and...

11. #### Stokes Efficiency of Molecular Motor-Cargo Systems

Wang, Hongyun; Zhou, Hong
A molecular motor utilizes chemical free energy to generate a unidirectional motion through the viscous fluid. In many experimental settings and biological settings, a molecular motor is elastically linked to a cargo. The stochastic motion of a molecular motor-cargo system is governed by a set of Langevin equations, each corresponding to an individual chemical occupancy state. The change of chemical occupancy state is modeled by a continuous time discrete space Markov process. The probability density of a motor-cargo system is governed by a two-dimensional Fokker-Planck equation. The operation of a molecular motor is dominated by high viscous friction and large thermal fluctuations from surrounding fluid. The instantaneous velocity...

12. #### A Class of Nonlinear Integral Operators Preserving Double Subordinations

Kwon, Oh Sang; Cho, Nak Eun
The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain integral operators defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also considered.

13. #### $q$ -Genocchi Numbers and Polynomials Associated with Fermionic $p$ -Adic Invariant Integrals on ${\mathbb{Z}}_{p}$

Jang, Leechae; Kim, Taekyun
The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic $p$ -adic invariant integral on ${\mathbb{Z}}_{p}$ , we construct $p$ -adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: ${G}_{n+k,q}^{(k)}(x)={2}^{k}k!\big(\begin{smallmatrix}n+k\\ \vspace{0pt}k\end{smallmatrix}\big){\sum{}}_{l=0}^{\infty{}}{\sum{}}_{{d}_{0}+{d}_{1}+\cdots{}+{d}_{k}=k-1,{d}_{i}\in{}\mathbb{N}}{(-1)}^{l}{(l+x)}^{n} , where${G}_{n+k,q}^{(k)}(x)$are the$q$-Genocchi polynomials of order$k$. 14. ####$q$-Analogue of Wright Function El-Shahed, Moustafa; Salem, Ahmed We introduce a$q$-analogues of Wright function and its auxiliary functions as Barnes integral representations and series expansion. The relations between$q$-analogues of Wright function and some other functions are investigated. 15. #### Euler Numbers and Polynomials Associated with Zeta Functions Kim, Taekyun For$s\in{}\mathbb{C}$, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by${\zeta{}}_{E}(s)=2{\sum{}}_{n=1}^{\infty{}}({(-1)}^{n}/{n}^{s})$, and${\zeta{}}_{E}(s,x)=2{\sum{}}_{n=0}^{\infty{}}({(-1)}^{n}/{(n+x)}^{s})$. Thus, we note that the Euler zeta functions are entire functions in whole complex$s$-plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is,${\zeta{}}_{E}(-k)={E}_{k}^{\ast}$, and${\zeta{}}_{E}(-k,x)={E}_{k}^{\ast}(x)$. We give some interesting identities between the Euler numbers and the zeta functions. Finally, we will give the new values of the Euler zeta function at positive even integers. 16. #### Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains Amendola, M. E.; Rossi, L.; Vitolo, A. We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem. 17. #### Models of Function Type for Commutative Symmetric Operator Families in Krein Spaces Strauss, Vladimir Commutative symmetric operator families of the so-called${D}_{\kappa}^{+}$-class are considered in Krein spaces. It is proved that the restriction of a family of this type on a special kind of invariant subspace is similar to a family of operators adjoint to multiplication operators by scalar functions acting on a suitable function space. 18. #### Pairwise Weakly Regular-Lindelöf Spaces Kılıçman, Adem; Salleh, Zabidin We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regular-Lindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish some of their relations. 19. #### Approximation of Generalized Left Derivations Kang, Sheon-Young; Chang, Ick-Soon We need to take account of the superstability for generalized left derivations (resp., generalized derivations) associated with a Jensen-type functional equation, and we also deal with problems for the Jacobson radical ranges of left derivations (resp., derivations). 20. #### A Functional Equation Originating from Elliptic Curves Park, Won-Gil; Bae, Jae-Hyeong We obtain the general solution and the stability of the functional equation$f(x+y+z,u+v+w)+f(x+y-z,u+v+w)+2f(x,u-w)+2f(y,v-w)=f(x+y,u+w)+f(x+y,v+w)+f(x+z,u+w)+f(x-z,u+v-w)+f(y+z,v+w)+f(y-z,u+v-w)$. The function$f(x,y)={x}^{3}+ax+b-{y}^{2}\$ having level curves as elliptic curves is a solution of the above functional equation.

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